Question

In the given figure, O is the centre of the circle and ∠ABC = 55°. Calculate the values of x and y.

Answer 1

∠AOC = 2∠ABC = 2 × 55°

(Angle at the centre is double the angle at the circumference subtended by the same chord)

∴ x = 110°

ABCD is cyclic quadrilateral

∴ ∠ADC + ∠ABC = 180°

(Pair of opposite angles in a cyclic quadrilateral are supplementary

`=>` y = 180° – 55° = 125°